Integrand size = 34, antiderivative size = 34 \[ \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\text {Int}\left (\frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx \\ \end{align*}
Not integrable
Time = 0.10 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.06 \[ \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx \]
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Not integrable
Time = 0.72 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00
\[\int \frac {\left (b g x +a g \right )^{2}}{A +B \ln \left (\frac {e \left (b x +a \right )^{2}}{\left (d x +c \right )^{2}}\right )}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.21 \[ \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int { \frac {{\left (b g x + a g\right )}^{2}}{B \log \left (\frac {{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A} \,d x } \]
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Not integrable
Time = 14.06 (sec) , antiderivative size = 258, normalized size of antiderivative = 7.59 \[ \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=g^{2} \left (\int \frac {a^{2}}{A + B \log {\left (\frac {a^{2} e}{c^{2} + 2 c d x + d^{2} x^{2}} + \frac {2 a b e x}{c^{2} + 2 c d x + d^{2} x^{2}} + \frac {b^{2} e x^{2}}{c^{2} + 2 c d x + d^{2} x^{2}} \right )}}\, dx + \int \frac {b^{2} x^{2}}{A + B \log {\left (\frac {a^{2} e}{c^{2} + 2 c d x + d^{2} x^{2}} + \frac {2 a b e x}{c^{2} + 2 c d x + d^{2} x^{2}} + \frac {b^{2} e x^{2}}{c^{2} + 2 c d x + d^{2} x^{2}} \right )}}\, dx + \int \frac {2 a b x}{A + B \log {\left (\frac {a^{2} e}{c^{2} + 2 c d x + d^{2} x^{2}} + \frac {2 a b e x}{c^{2} + 2 c d x + d^{2} x^{2}} + \frac {b^{2} e x^{2}}{c^{2} + 2 c d x + d^{2} x^{2}} \right )}}\, dx\right ) \]
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Not integrable
Time = 0.22 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.06 \[ \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int { \frac {{\left (b g x + a g\right )}^{2}}{B \log \left (\frac {{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A} \,d x } \]
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Not integrable
Time = 0.53 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.06 \[ \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int { \frac {{\left (b g x + a g\right )}^{2}}{B \log \left (\frac {{\left (b x + a\right )}^{2} e}{{\left (d x + c\right )}^{2}}\right ) + A} \,d x } \]
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Not integrable
Time = 2.27 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.06 \[ \int \frac {(a g+b g x)^2}{A+B \log \left (\frac {e (a+b x)^2}{(c+d x)^2}\right )} \, dx=\int \frac {{\left (a\,g+b\,g\,x\right )}^2}{A+B\,\ln \left (\frac {e\,{\left (a+b\,x\right )}^2}{{\left (c+d\,x\right )}^2}\right )} \,d x \]
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